# Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

**Solution:**

We know that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

AB is the height of one pole = 6m

CD is the height of another pole = 11m

AC is the distance between two poles at bottom = 12m

BD is the distance between the tops of the poles = ?

Draw BE || AC

Now consider, in Δ BED

∠BED = 90°

BE = AC = 12 m

DE = CD - CE

DE = 11 - 6 = 5 cm

Now,

BD^{2} = BE^{2} + DE^{2 } (Pythagoras therorem)

BD^{2} = 12^{2} + 5^{2}

BD^{2} = 144 + 25

BD^{2} = 169

BD = 13m

The distance between the top of the poles is 13 m.

**Video Solution:**

## Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.5 Question 12:

**Summary:**

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, then the distance between their tops is 13 m.